## Abstract

Time-varying graphs (T-graph) consist of a time-evolving set of graph snapshots (or graphlets). A T-graph property with potential applications in both computer and social network forensics is T-reachability, which identifies the nodes reachable from a source node using the T-graph edges over time period T. In this paper, we consider the problem of estimating the T-reachable set of a source node in two different settings - when a time-evolution of a T-graph is specified by a probabilistic model, and when the actual T-graph snapshots are known and given to us offline ("data aware" setting). Since the value of T could be large in many applications, we propose two simple techniques, namely T-graph sampling and T-graph smashing for significantly reducing the complexity of this computation, while minimizing the estimation error. We show that for the data-aware case, both T-graph sampling and smashing problems are NP-hard, but they are amenable to reasonably good approximations. We also showthat for the probabilistic setting where each graphlet in a T-graph is an Erdos-Renyi random graph, sampling yields a loose lower bound for the T-reachable set, while different styles of smashing yield more useful upper and lower bounds. Finally, we show that our algorithms (both dataaware and data-oblivious) can estimate the T-reachable set in real world time-varying networks within reasonable accuracy using less than 0.5% of the number of graphlets.

Original language | English |
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Title of host publication | SIAM International Conference on Data Mining 2014, SDM 2014 |

Editors | Mohammed Zaki, Zoran Obradovic, Pang Ning-Tan, Arindam Banerjee, Chandrika Kamath, Srinivasan Parthasarathy |

Publisher | Society for Industrial and Applied Mathematics Publications |

Pages | 983-991 |

Number of pages | 9 |

ISBN (Electronic) | 9781510811515 |

DOIs | |

State | Published - 2014 |

Externally published | Yes |

Event | 14th SIAM International Conference on Data Mining, SDM 2014 - Philadelphia, United States Duration: 24 Apr 2014 → 26 Apr 2014 |

### Publication series

Name | SIAM International Conference on Data Mining 2014, SDM 2014 |
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Volume | 2 |

### Conference

Conference | 14th SIAM International Conference on Data Mining, SDM 2014 |
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Country/Territory | United States |

City | Philadelphia |

Period | 24/04/14 → 26/04/14 |

### Bibliographical note

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